Section 2
PROCESSES
3. Strategic Capacity Management
4. Manufacturing Processes
5. Services Processes
6. Six-Sigma Quality
PROCESSES
The second section of Operations and Supply Man-
and read the paper? Have you ever thought about how
agement: The Core is centered on the design and
the tasks should be ordered or what the best way to
analysis of business processes. Maybe becoming an
execute each task is? In making these decisions you are
efficiency expert is not your dream, but it is important
allocating your own personal capacity.*
to learn the fundamentals. Have you ever wondered
This section is about designing efficient processes
why you always have to wait in line at one store but
and allocating capacity for all types of businesses.
another one seems to be on top of the crowds? The
Companies also need to develop a quality philosophy
key to serving customers well, whether with products
and integrate it into their processes. Actually, quality
or with services, is having a great process.
and process efficiency are closely related. Have you
We use processes to do most things. You probably
ever done something but then had to do it again be-
have a regular process that you use every morning.
cause it was not done properly the first time? This sec-
What are the tasks associated with your process? Do
tion considers these subjects in both manufacturing
you brush your teeth, take a shower, dress, make coffee,
and service industries.
*The original version of the movie “Cheaper by the Dozen” made in the 1950s was based upon the life of Frank Gilbreth who invented
motion study in the 1900s. Gilbreth was so concerned with personal efficiency that he did a study of whether it was faster and more
accurate to button one’s seven button vest from the bottom up or the top down. (Answer: bottom up!)
Chapter 3
STRATEGIC CAPACITY
MANAGEMENT
After reading the chapter you will:
1. Know what the concept of capacity is and how important it is to “manage” capacity
over time.
2. Understand the impact of economies of scale on the capacity of a firm.
3. Understand what a learning curve is and how to analyze one.
4. Understand how to use decision trees to analyze alternatives when faced with the
problem of adding capacity.
5. Understand the differences in planning capacity between manufacturing firms and
service firms.
52
Shouldice Hospital: Hernia Surgery Innovation
53
Capacity Management in Operations
Capacity defined
Strategic capacity planning defined
54
Capacity Planning Concepts
Economies and Diseconomies of Scale
Capacity Focus
Capacity Flexibility
56
Best operating level defined
Capacity utilization rate defined
Capacity Focus defined
Economies of scope defined
The Learning Curve
Plotting Learning Curves
Logarithmic Analysis
Learning Curve Tables
61
Learning curve defined
Capacity Planning
Considerations in Adding Capacity
Capacity cushion defined
Determining Capacity Requirements
Using Decision Trees to Evaluate Capacity Alternatives
68
Planning Service Capacity
Capacity Planning in Service versus Manufacturing
Capacity Utilization and Service Quality
70
Summary
77
Case: Shouldice Hospital—A Cut Above
S H O U L D I C E H O S P I TA L : H E R N I A
S U R G E RY I N N O VAT I O N
During World War II, Dr. Edward Earle Shouldice, a major in the army, found that many young
men willing to serve their country had to be denied enlistment because they needed surgical
treatment to repair hernias before they could be pronounced physically fit for military training. In 1940, hospital space and doctors were scarce, especially for a nonemergency surgery
that normally took three weeks of hospitalization. So, Dr. Shouldice resolved to do what he
could to alleviate the problem. Contributing his services at no fee, he performed an innovative method of surgery on 70 of those men, speeding their induction into the army.
The recruits made their success
stories known, and by the war’s end,
more than 200 civilians had contacted the doctor and were awaiting
surgery. The limited availability of
hospitals beds, however, created a
major problem. There was only one
solution: Dr. Shouldice decided to
open his own hospital.
In July 1945, Shouldice Hospital,
with a staff consisting of a nurse, a
secretary, and a cook, opened its
doors to its waiting patients. In a single operating room, Dr. Shouldice repaired two hernias per day. As requests for this surgery increased, Dr. Shouldice extended
the facilities, located on Church Street in Toronto, by eventually buying three adjacent
buildings and increasing the staff accordingly. In 1953, he purchased a country estate in
Thornhill, where a second hospital was established.
Today all surgery takes place in Thornhill. Repeated development has culminated in the
present 89-bed facility. Shouldice Hospital has been dedicated to the repair of hernias for
over 55 years, using the “Shouldice Technique.” The “formula,” although not a secret, extends beyond the skill of surgeons and their ability to perform to the Shouldice standard.
Shouldice Hospital is a total environment. Study the capacity problems with this special
type of hospital in the case at the end of this chapter.
Source: Summarized from www.shouldice.com.
STRATEGIC CAPACITY MANAGEMENT
chapter 3
53
Manufacturing and service capacity investment decisions can be very complex. Consider
some of the following difficult questions that need to be addressed:
• How long will it take to bring new capacity on stream? How does this match with the
time that it takes to develop a new product?
• What will be the impact of not having sufficient capacity in the supply chain for a
promising product?
• Should the firm use third-party contract manufacturers? How much of a premium will
the contract manufacturer charge for providing flexibility in manufacturing volume?
In this chapter, we look at these tough strategic capacity decisions. We begin by discussing
the nature of capacity from an OM perspective.
C A PAC I T Y M A N AG E M E N T
I N O P E R AT I O N S
A dictionary definition of capacity is “the ability to hold, receive, store, or accommodate.”
In a general business sense, it is most frequently viewed as the amount of output that a system is capable of achieving over a specific period of time. In a service setting, this might
be the number of customers that can be handled between noon and 1:00 P.M. In manufacturing, this might be the number of automobiles that can be produced in a single shift.
When looking at capacity, operations managers need to look at both resource inputs
and product outputs. The reason is that, for planning purposes, real (or effective) capacity
depends on what is to be produced. For example, a firm that makes multiple products
inevitably can produce more of one kind than of another with a given level of resource inputs.
Thus, while the managers of an automobile factory may state that their facility has 6,000 production hours available per year, they are also thinking that these hours can be used to make
either 150,000 two-door models or 120,000 four-door models (or some mix of the two- and
four-door models). This reflects their knowledge of what their current technology and labor
force inputs can produce and the product mix that is to be demanded from these resources.
An operations management view also emphasizes the time dimension of capacity. That is,
capacity must also be stated relative to some period of time. This is evidenced in the common
distinction drawn between long-range, intermediate-range, and short-range capacity planning.
Capacity planning is generally viewed in three time durations:
Long range—greater than one year. Where productive resources (such as buildings,
equipment, or facilities) take a long time to acquire or dispose of, long-range capacity
planning requires top management participation and approval.
Intermediate range—monthly or quarterly plans for the next 6 to 18 months. Here, capacity may be varied by such alternatives as hiring, layoffs, new tools, minor equipment
purchases, and subcontracting.
Short range—less than one month. This is tied into the daily or weekly scheduling
process and involves making adjustments to eliminate the variance between planned
and actual output. This includes alternatives such as overtime, personnel transfers, and
alternative production routings.
Although there is no one person with the job title “capacity manager,” there are several
managerial positions charged with the effective use of capacity. Capacity is a relative term; in
an operations management context, it may be defined as the amount of resource inputs available relative to output requirements over a particular period of time. Note that this definition
Capacity
Service
Cross
Functional
54
section 2
PROCESSES
JELLY BELLY CANDY COMPANY,
HEADQUARTERED IN FAIRFIELD,
CALIFORNIA, PRODUCES
100,000 POUNDS OF JELLY
BELLY BEANS PER DAY,
APPROXIMATELY 347 BEANS PER
SECOND. IT TAKES 7 TO 21
DAYS OF CURING ON THESE
TRAYS TO MAKE A JELLY
BELLY
BEAN.
Strategic capacity
planning
makes no distinction between efficient and inefficient use of capacity. In this respect, it is
consistent with how the federal Bureau of Economic Analysis defines maximum practical
capacity used in its surveys: “That output attained within the normal operating schedule of
shifts per day and days per week including the use of high-cost inefficient facilities.”
The objective of strategic capacity planning is to provide an approach for determining
the overall capacity level of capital-intensive resources—facilities, equipment, and overall labor force size—that best supports the company’s long-range competitive strategy. The
capacity level selected has a critical impact on the firm’s response rate, its cost structure,
its inventory policies, and its management and staff support requirements. If capacity is
inadequate, a company may lose customers through slow service or by allowing competitors to enter the market. If capacity is excessive, a company may have to reduce prices to
stimulate demand; underutilize its workforce; carry excess inventory; or seek additional,
less profitable products to stay in business.
C A PAC I T Y P L A N N I N G C O N C E P T S
Best operating level
Capacity utilization
rate
The term capacity implies an attainable rate of output, for example, 480 cars per day, but
says nothing about how long that rate can be sustained. Thus, we do not know if this 480 cars
per day is a one-day peak or a six-month average. To avoid this problem, the concept of
best operating level is used. This is the level of capacity for which the process was designed
and thus is the volume of output at which average unit cost is minimized. Determining this
minimum is difficult because it involves a complex trade-off between the allocation of fixed
overhead costs and the cost of overtime, equipment wear, defect rates, and other costs.
An important measure is the capacity utilization rate, which reveals how close a firm
is to its best operating level:
Capacity utilization rate =
Capacity used
Best operating level
So, for example, if our plant’s best operating level were 500 cars per day and the plant was
currently operating at 480 cars per day, the capacity utilization rate would be 96 percent.
Capacity utilization rate =
480
= .96 or 96%
500
STRATEGIC CAPACITY MANAGEMENT
55
chapter 3
The capacity utilization rate is expressed as a percentage and requires that the numerator
and denominator be measured in the same units and time periods (such as machine
hours/day, barrels of oil/day, dollars of output/day).
Economies and Diseconomies of Scale
The basic notion of economies of scale is that as a plant gets larger and volume increases,
the average cost per unit of output drops. This is partially due to lower operating and capital
cost, because a piece of equipment with twice the capacity of another piece typically does
not cost twice as much to purchase or operate. Plants also gain efficiencies when they
become large enough to fully utilize dedicated resources (people and equipment) for information technology, material handling, and administrative support.
At some point, the size of a plant becomes too large and diseconomies of scale become
a problem. These diseconomies may surface in many different ways. For example,
maintaining the demand required to keep the large facility busy may require significant
discounting of the product. The U.S. automobile manufacturers continually face this
problem. Another typical example involves using a few large-capacity pieces of equipment. Minimizing equipment downtime is essential in this type of operation. M&M Mars,
for example, has highly automated, high-volume equipment to make M&Ms. A single
packaging line moves 2.6 million M&Ms each hour. Even though direct labor to operate
the equipment is very low, the labor required to maintain the equipment is high.
In many cases, the size of a plant may be influenced by factors other than the internal
equipment, labor, and other capital expenditures. A major factor may be the cost to transport raw materials and finished product to and from the plant. A cement factory, for example, would have a difficult time serving customers more than a few hours from its plant.
Analogously, automobile companies such as Ford, Honda, Nissan, and Toyota have found
it advantageous to locate plants within specific international markets. The anticipated size
of these intended markets will largely dictate the size and capacity of the plants.
Jaguar, the luxury automobile producer, recently found they had too many plants.
Jaguar was employing 8,560 workers in three plants that produced 126,122 cars, about 14
cars per employee. In comparison, Volvo’s plant in Torslanda, Sweden, was more than
twice as productive, building 158,466 cars with 5,472 workers, or 29 cars per employee.
By contrast, BMW AG’s Mini unit made 174,000 vehicles at a single British plant with just
4,500 workers (39 cars per employee).
Global
Capacity Focus
The concept of the focused factory holds that a production facility works best when it focuses
on a fairly limited set of production objectives. This means, for example, that a firm should not
expect to excel in every aspect of manufacturing performance: cost, quality, delivery speed
and reliability, changes in demand, and flexibility to adapt to new products. Rather, it should
select a limited set of tasks that contribute the most to corporate objectives. However, given
the breakthroughs in manufacturing technology, there is an evolution in factory objectives
toward trying to do everything well. How do we deal with these apparent contradictions? One
way is to say that if the firm does not have the technology to master multiple objectives, then
a narrow focus is the logical choice. Another way is to recognize the practical reality that not
all firms are in industries that require them to use their full range of capabilities to compete.
The capacity focus concept can also be operationalized through the mechanism of plants
within plants—or PWPs. A focused plant may have several PWPs, each of which may have
separate suborganizations, equipment and process policies, workforce management policies,
production control methods, and so forth for different products—even if they are made under
the same roof. This, in effect, permits finding the best operating level for each department of
the organization and thereby carries the focus concept down to the operating level.
Capacity focus
56
section 2
PROCESSES
THE XEROX FOCUSED FACTORY
CREATES A FLEXIBLE AND
EFFICIENT WORK ENVIRONMENT
WHERE TEAMS OF EMPLOYEES
ARE RESPONSIBLE FOR THE
END-TO-END MANUFACTURING
OF SPECIFIC PRODUCTS. THE
FACTORY WAS DESIGNED WITH
INPUT FROM THE INDUSTRIAL
STAFF, WORKING IN TANDEM
WITH ENGINEERS AND
MANAGEMENT.
Capacity Flexibility
Capacity flexibility means having the ability to rapidly increase or decrease production
levels, or to shift production capacity quickly from one product or service to another. Such
flexibility is achieved through flexible plants, processes, and workers, as well as through
strategies that use the capacity of other organizations. Increasingly, companies are taking
the idea of flexibility into account as they design their supply chains. Working with suppliers, they can build capacity into their whole systems.
F l e x i b l e P l a n t s Perhaps the ultimate in plant flexibility is the zero-changeovertime plant. Using movable equipment, knockdown walls, and easily accessible and
reroutable utilities, such a plant can quickly adapt to change. An analogy to a familiar
service business captures the flavor well: a plant with equipment “that is easy to install and
easy to tear down and move—like the Ringling Bros.–Barnum and Bailey Circus in the old
tent-circus days.”
Economies of
scope
F l e x i b l e P r o c e s s e s Flexible processes are epitomized by flexible manufacturing
systems on the one hand and simple, easily set up equipment on the other. Both of these
technological approaches permit rapid low-cost switching from one product to another,
enabling what are sometimes referred to as economies of scope. (By definition, economies
of scope exist when multiple products can be produced at a lower cost in combination than
they can separately.)
F l e x i b l e W o r k e r s Flexible workers have multiple skills and the ability to switch
easily from one kind of task to another. They require broader training than specialized
workers and need managers and staff support to facilitate quick changes in their work
assignments.
THE LEARNING CURVE
Learning curve
A well-known concept is the learning curve. A learning curve is a line displaying the relationship between unit production and the cumulative number of units produced. As plants
produce more, they gain experience in the best production methods, which reduce their
costs of production in a predictable manner. Every time a plant’s cumulative production
doubles, its production costs decline by a specific percentage depending on the nature of
STRATEGIC CAPACITY MANAGEMENT
exhibit 3.1
The Learning Curve
a. Costs per unit produced fall by a specific percentage
each time cumulative production doubles. This relationship can be expressed through a linear scale as
shown in this graph of 90 percent learning curve:
57
chapter 3
b. It can also be expressed through logarithms:
(A Log-Log Scale)
.32
.32
.30
.30
Cost or
price per .28
unit ($)
.26
.28
Cost or
price per .26
unit ($)
.24
.24
0
400
800
1200
1600
Total accumulated production of units (1,000)
0
200
400
800
1600
Total accumulated production of units (1,000)
the business. Exhibit 3.1 demonstrates the effect of a learning curve on the production costs
of hamburgers.
The learning curve percentage varies across industries. To apply this concept to the
restaurant industry, consider a hypothetical fast-food chain that has produced 5 million
hamburgers. Given a current variable cost of $0.55 per burger, what will the cost per burger
be when cumulative production reaches 10 million burgers? If the firm has a 90 percent
learning curve, costs will fall to 90 percent of $0.55, or $0.495, when accumulated production reaches 10 million. At 1 billion hamburgers, the variable cost drops to less
than $0.25.
Note that sales volume becomes an important issue in achieving cost savings. If firm
A serves twice as many hamburgers daily as firm B, it will accumulate “experience” twice
as fast.
Learning curve theory is based on three assumptions:
1. The amount of time required to complete a given task or unit of a product will be
less each time the task is undertaken.
2. The unit time will decrease at a decreasing rate.
3. The reduction in time will follow a predictable pattern.
Each of these assumptions was found to hold true in the airplane industry, where learning
curves were first applied. In this application, it was observed that, as output doubled, there was
a 20 percent reduction in direct production worker-hours per unit between doubled units.
Thus, if it took 100,000 hours for Plane 1, it would take 80,000 hours for Plane 2, 64,000 hours
for Plane 4, and so forth. Because the 20 percent reduction meant that, say, Unit 4 took only
80 percent of the production time required for Unit 2, the line connecting the coordinates of
output and time was referred to as an “80 percent learning curve.” (By convention, the percentage learning rate is used to denote any given exponential learning curve.)
A learning curve may be developed from an arithmetic tabulation, by logarithms, or by
some other curve-fitting method, depending on the amount and form of the available data.
58
exhibit 3.2
section 2
PROCESSES
Learning Curves Plotted as Times and Numbers of Units
A.
B.
Cumulative average time
Output per
time period
Time
per
unit
Observed
data
Fitted line
Unit number
A Progress Curve
Interactive
Operations
Management
Average output during
a time period in
the future
Time
Industrial Learning
There are two ways to think about the improved performance that comes with learning
curves: time per unit (as in Exhibit 3.2A) or units of output per time period (as in 3.2B).
Time per unit shows the decrease in time required for each successive unit. Cumulative
average time shows the cumulative average performance times as the total number of units
increases. Time per unit and cumulative average times are also called progress curves or
product learning and are useful for complex products or products with a longer cycle time.
Units of output per time period is also called industry learning and is generally applied to
high-volume production (short cycle time).
Note in Exhibit 3.2A that the cumulative average curve does not decrease as fast as the
time per unit because the time is being averaged. For example, if the time for Units 1, 2, 3,
and 4 were 100, 80, 70, and 64, they would be plotted that way on the time per unit graph,
but would be plotted as 100, 90, 83.3, and 78.5 on the cumulative average time graph.
Plotting Learning Curves
There are many ways to analyze past data to fit a useful trend line. We will use the simple exponential curve first as an arithmetic procedure and then by a logarithmic analysis.
In an arithmetical tabulation approach, a column for units is created by doubling, row by
row, as 1, 2, 4, 8, 16. . . . The time for the first unit is multiplied by the learning percentage to obtain the time for the second unit. The second unit is multiplied by the learning percentage for the fourth unit, and so on. Thus, if we are developing an 80 percent
learning curve, we would arrive at the figures listed in column 2 of Exhibit 3.3. Because
it is often desirable for planning purposes to know the cumulative direct labor hours,
column 4, which lists this information, is also provided. The calculation of these figures
is straightforward; for example, for Unit 4, cumulative average direct labor hours would
be found by dividing cumulative direct labor hours by 4, yielding the figure given in
column 4.
Exhibit 3.4A shows three curves with different learning rates: 90 percent, 80 percent,
and 70 percent. Note that if the cost of the first unit was $100, the 30th unit would cost
$59.63 at the 90 percent rate and $17.37 at the 70 percent rate. Differences in learning rates
can have dramatic effects.
In practice, learning curves are plotted using a graph with logarithmic scales. The unit
curves become linear throughout their entire range and the cumulative curve becomes
linear after the first few units. The property of linearity is desirable because it facilitates extrapolation and permits a more accurate reading of the cumulative curve. This type of scale
STRATEGIC CAPACITY MANAGEMENT
Unit, Cumulative, and Cumulative Average Direct Labor Worker-Hours Required for an
80 Percent Learning Curve
(1)
UNIT
NUMBER
(2)
UNIT DIRECT
LABOR HOURS
(3)
CUMULATIVE DIRECT
LABOR HOURS
(4)
CUMULATIVE AVERAGE
DIRECT LABOR HOURS
1
100,000
100,000
100,000
2
80,000
180,000
90,000
4
64,000
314,210
78,553
8
51,200
534,591
66,824
16
40,960
892,014
55,751
32
32,768
1,467,862
45,871
64
26,214
2,392,453
37,382
128
20,972
3,874,395
30,269
256
16,777
6,247,318
24,404
59
chapter 3
exhibit 3.3
Excel:
Learning
Curves
is an option in Microsoft Excel. Simply generate a regular scatter plot in your spreadsheet
and then select each axis and format the axis with the logarithmic option. Exhibit 3.4B
shows the 80 percent unit cost curve and average cost curve on a logarithmic scale. Note
that the cumulative average cost is essentially linear after the eighth unit.
Although the arithmetic tabulation approach is useful, direct logarithmic analysis of
learning curve problems is generally more efficient because it does not require a complete
enumeration of successive time–output combinations. Moreover, where such data are not
available, an analytical model that uses logarithms may be the most convenient way of
obtaining output estimates.
exhibits 3.4
3.4A—Arithmetic Plot of 70, 80, and 90 Percent Learning Curves
3.4B—Logarithmic Plot of an 80 Percent Learning Curve
20
$100
90
Production cost ($)
80
70
90% Learning
curve
10
9
8
7
6
5
4
80%
3
60
50
40
30
20
10
0
70%
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
Unit number
Average cost/unit
(cumulative)
Cost for a
particular unit
2
1
1
2
3 4 5 6 78910
20 30 40 50 60 80 100 200 300 400 600 1,000
Unit number
Excel:
Learning
Curves
60
section 2
PROCESSES
Logarithmic Analysis
The normal form of the learning curve equation is
Yx = K x n
[3.1]
where
x = Unit number
Yx = Number of direct labor hours required to produce the xth unit
K = Number of direct labor hours required to produce the first unit
n = log b/log 2 where b = Learning percentage
We can solve this mathematically or by using a table, as shown in the next section.
Mathematically, to find the labor-hour requirement for the eighth unit in our example
(Exhibit 3.3), we would substitute as follows:
Y8 = (100,000)(8)n
Using logarithms:
Y8 = 100,000(8)log 0.8/log 2
= 100,000(8)−0.322 =
=
100,000
(8)0.322
100,000
= 51,192
1.9535
Therefore, it would take 51,192 hours to make the eighth unit. (See the spreadsheet
“Learning Curves.”)
L e a r n i n g C u r v e Ta b l e s
Excel:
Learning
Curves
When the learning percentage is known, the tables in Appendix B can be easily used to calculate estimated labor hours for a specific unit or for cumulative groups of units. We need
only multiply the initial unit labor hour figure by the appropriate tabled value.
To illustrate, suppose we want to double-check the figures in Exhibit 3.3 for unit and cumulative labor hours for Unit 16. From Appendix Exhibit B.1, the unit improvement factor
for Unit 16 at 80 percent is .4096. This multiplied by 100,000 (the hours for Unit 1) gives
40,960, the same as in Exhibit 3.3. From Appendix Exhibit B.2, the cumulative improvement factor for cumulative hours for the first 16 units is 8.920. When multiplied by
100,000, this gives 892,000, which is reasonably close to the exact value of 892,014 shown
in Exhibit 3.3.
The following is a more involved example of the application of a learning curve to a
production problem.
Example 3.1: Sample Learning Curve Problem
Captain Nemo, owner of the Suboptimum Underwater Boat Company (SUB), is puzzled. He has a
contract for 11 boats and has completed 4 of them. He has observed that his production manager, young
Mr. Overick, has been reassigning more and more people to torpedo assembly after the construction of
the first four boats. The first boat, for example, required 225 workers, each working a 40-hour week,
STRATEGIC CAPACITY MANAGEMENT
chapter 3
while 45 fewer workers were required for the second boat. Overick has told them that “this is just the
beginning” and that he will complete the last boat in the current contract with only 100 workers!
Overick is banking on the learning curve, but has he gone overboard?
SOLUTION
Because the second boat required 180 workers, a simple exponential curve shows that the learning
percentage is 80 percent (180 ÷ 225). To find out how many workers are required for the 11th boat,
we look up unit 11 for an 80 percent improvement ratio in Appendix Exhibit B.1 and multiply this
value by the number required for the first sub. By interpolating between Unit 10 and Unit 12 we find
the improvement ratio is equal to .4629. This yields 104.15 workers (.4269 interpolated from table ×
225). Thus, Overick’s estimate missed the boat by four people.
•
Example 3.2: Estimating Cost Using Learning Curves
SUB has produced the first unit of a new line of minisubs at a cost of $500,000—$200,000 for
materials and $300,000 for labor. It has agreed to accept a 10 percent profit, based on cost, and it is
willing to contract on the basis of a 70 percent learning curve. What will be the contract price for
three minisubs?
SOLUTION
Cost of first sub
Cost of second sub
Materials
Labor: $300,000 × .70
Cost of third sub
Materials
Labor: $300,000 × .5682
Total cost
Markup: $1,280,460 × .10
Selling price
$ 500,000
$200,000
210,000
200,000
170,460
410,000
370,460
1,280,460
128,046
$1,408,506
If the operation is interrupted, then some relearning must occur. How far to go back up the learning curve can be estimated in some cases.
•
C A PAC I T Y P L A N N I N G
Considerations in Adding Capacity
Many issues must be considered when adding capacity. Three important ones are maintaining system balance, frequency of capacity additions, and the use of external capacity.
M a i n t a i n i n g S y s t e m B a l a n c e In a perfectly balanced plant, the output of
stage 1 provides the exact input requirement for stage 2. Stage 2’s output provides the exact
input requirement for stage 3, and so on. In practice, however, achieving such a “perfect”
design is usually both impossible and undesirable. One reason is that the best operating
levels for each stage generally differ. For instance, department 1 may operate most
efficiently over a range of 90 to 110 units per month, whereas department 2, the next stage
61
62
Supply
Chain
section 2
PROCESSES
in the process, is most efficient at 75 to 85 units per month, and department 3 works best
over a range of 150 to 200 units per month. Another reason is that variability in product
demand and the processes themselves generally leads to imbalance except in automated
production lines, which, in essence, are just one big machine.
There are various ways of dealing with imbalance. One is to add capacity to stages that
are bottlenecks. This can be done by temporary measures such as scheduling overtime,
leasing equipment, or purchasing additional capacity through subcontracting. A second
way is through the use of buffer inventories in front of the bottleneck stage to ensure that it
always has something to work on. A third approach involves duplicating the facilities of
one department on which another is dependent. All these approaches are increasingly being
applied to supply chain design. This supply planning also helps reduce imbalances for supplier partners and customers.
F r e q u e n c y o f C a p a c i t y A d d i t i o n s There are two types of costs to consider
when adding capacity: the cost of upgrading too frequently and that of upgrading too
infrequently. Upgrading capacity too frequently is expensive. Direct costs include
removing and replacing old equipment and training employees on the new equipment. In
addition, the new equipment must be purchased, often for considerably more than the
selling price of the old. Finally, there is the opportunity cost of idling the plant or service
site during the changeover period.
Conversely, upgrading capacity too infrequently is also expensive. Infrequent expansion means that capacity is purchased in larger chunks. Any excess capacity that is
purchased must be carried as overhead until it is utilized. (Exhibit 3.5 illustrates frequent
versus infrequent capacity expansion.)
E x t e r n a l S o u r c e s o f O p e r a t i o n s a n d S u p p l y C a p a c i t y In some
cases, it may be cheaper to not add capacity at all, but rather to use some existing external
source of capacity. Two common strategies used by organizations are outsourcing and
exhibit 3.5
Frequent versus Infrequent Capacity Expansion
Demand
forecast
Capacity level
(infrequent expansion)
Capacity level
(frequent expansion)
Volume
Small chunk
Years
Large chunk
STRATEGIC CAPACITY MANAGEMENT
63
chapter 3
sharing capacity. An example of outsourcing is Japanese banks in California subcontracting
check-clearing operations. An example of sharing capacity is two domestic airlines flying
different routes with different seasonal demands exchanging aircraft (suitably repainted)
when one’s routes are heavily used and the other’s are not. A new twist is airlines sharing
routes—using the same flight number even though the airline company may change through
the route. Outsourcing is covered in more depth in Chapter 7.
Determining Capacity Requirements
In determining capacity requirements, we must address the demands for individual product
lines, individual plant capabilities, and allocation of production throughout the plant network. Typically this is done according to the following steps:
1. Use forecasting techniques (see Chapter 10) to predict sales for individual products
within each product line.
2. Calculate equipment and labor requirements to meet product line forecasts.
3. Project labor and equipment availabilities over the planning horizon.
Often the firm then decides on some capacity cushion that will be maintained between
the projected requirements and the actual capacity. A capacity cushion is an amount of capacity in excess of expected demand. For example, if the expected annual demand on a facility is $10 million in products per year and the design capacity is $12 million per year, it
has a 20 percent capacity cushion. A 20 percent capacity cushion equates to an 83 percent
utilization rate (100%/120%).
When a firm’s design capacity is less than the capacity required to meet its demand, it is
said to have a negative capacity cushion. If, for example, a firm has a demand of $12 million in products per year but can produce only $10 million per year, it has a negative
capacity cushion of 16.7 percent.
We now apply these three steps to an example.
Capacity cushion
Example 3.3: Determining Capacity Requirements
The Stewart Company produces two flavors of salad dressings: Paul’s and Newman’s. Each is available in bottles and single-serving plastic bags. Management would like to determine equipment and
labor requirements for the next five years.
SOLUTION
Step 1. Use forecasting techniques to predict sales for individual products within each product line.
The marketing department, which is now running a promotional campaign for Newman’s dressing,
provided the following forecast demand values (in thousands) for the next five years. The campaign
is expected to continue for the next two years.
YEAR
PAUL’S
Bottles (000s)
Plastic bags (000s)
NEWMAN’S
Bottles (000s)
Plastic bags (000s)
1
2
3
4
5
60
100
100
200
150
300
200
400
250
500
75
200
85
400
95
600
97
650
98
680
Cross
Functional
64
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PROCESSES
Step 2. Calculate equipment and labor requirements to meet product line forecasts. Currently, three
machines that can package up to 150,000 bottles each per year are available. Each machine requires
two operators and can produce bottles of both Newman’s and Paul’s dressings. Six bottle machine
operators are available. Also, five machines that can package up to 250,000 plastic bags each per year
are available. Three operators are required for each machine, which can produce plastic bags of both
Newman’s and Paul’s dressings. Currently, 20 plastic bag machine operators are available.
Total product line forecasts can be calculated from the preceding table by adding the yearly
demand for bottles and plastic bags as follows:
YEAR
Excel:
Capacity
Bottles
Plastic bags
1
2
3
4
5
135
300
185
600
245
900
297
1,050
348
1,180
We can now calculate equipment and labor requirements for the current year (year 1). Because
the total available capacity for packaging bottles is 450,000/year (3 machines × 150,000 each), we
will be using 135/450 = 0.3 of the available capacity for the current year, or 0.3 × 3 = 0.9 machine.
Similarly, we will need 300/1,250 = 0.24 of the available capacity for plastic bags for the current
year, or 0.24 × 5 = 1.2 machines. The number of crew required to support our forecast demand for
the first year will consist of the crew required for the bottle and the plastic bag machines.
The labor requirement for year 1’s bottle operation is
0.9 bottle machine × 2 operators = 1.8 operators
1.2 bag machines × 3 operators = 3.6 operators
Step 3. Project labor and equipment availabilities over the planning horizon. We repeat the preceding calculations for the remaining years:
YEAR
1
PLASTIC BAG OPERATION
Percentage capacity utilized
Machine requirement
Labor requirement
BOTTLE OPERATION
Percentage capacity utilized
Machine requirement
Labor requirement
2
3
4
5
24
1.2
3.6
48
2.4
7.2
72
3.6
10.8
84
4.2
12.6
94
4.7
14.1
30
41
1.23
2.46
54
1.62
3.24
66
1.98
3.96
77
2.31
4.62
.9
1.8
A positive capacity cushion exists for all five years because the available capacity for both operations always exceeds the expected demand. The Stewart Company can now begin to develop the
intermediate-range or sales and operations plan for the two production lines. (See Chapter 11 for a
discussion of sales and operations planning.)
•
U s i n g D e c i s i o n Tre e s t o E va l u at e
Capacity Alternatives
A convenient way to lay out the steps of a capacity problem is through the use of decision
trees. The tree format helps not only in understanding the problem but also in finding a
solution. A decision tree is a schematic model of the sequence of steps in a problem and the
STRATEGIC CAPACITY MANAGEMENT
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65
conditions and consequences of each step. In recent years, a few commercial software
packages have been developed to assist in the construction and analysis of decision trees.
These packages make the process quick and easy.
Decision trees are composed of decision nodes with branches to and from them. Usually
squares represent decision points and circles represent chance events. Branches from decision points show the choices available to the decision maker; branches from chance events
show the probabilities for their occurrence.
In solving decision tree problems, we work from the end of the tree backward to the
start of the tree. As we work back, we calculate the expected values at each step. In calculating the expected value, the time value of money is important if the planning horizon
is long.
Once the calculations are made, we prune the tree by eliminating from each decision
point all branches except the one with the highest payoff. This process continues to the first
decision point, and the decision problem is thereby solved.
We now demonstrate an application to capacity planning for Hackers Computer
Store.
Example 3.4: Decision Trees
The owner of Hackers Computer Store is considering what to do with his business over the next five
years. Sales growth over the past couple of years has been good, but sales could grow substantially if a
major electronics firm is built in his area as proposed. Hackers’ owner sees three options. The first is to
enlarge his current store, the second is to locate at a new site, and the third is to simply wait and do nothing. The decision to expand or move would take little time, and, therefore, the store would not lose revenue. If nothing were done the first year and strong growth occurred, then the decision to expand would
be reconsidered. Waiting longer than one year would allow competition to move in and would make expansion no longer feasible.
The assumptions and conditions are as follows:
1. Strong growth as a result of the increased population of computer fanatics from the new electronics firm has a 55 percent probability.
2. Strong growth with a new site would give annual returns of $195,000 per year. Weak growth
with a new site would mean annual returns of $115,000.
3. Strong growth with an expansion would give annual returns of $190,000 per year. Weak
growth with an expansion would mean annual returns of $100,000.
4. At the existing store with no changes, there would be returns of $170,000 per year if there is
strong growth and $105,000 per year if growth is weak.
5. Expansion at the current site would cost $87,000.
6. The move to the new site would cost $210,000.
7. If growth is strong and the existing site is enlarged during the second year, the cost would still
be $87,000.
8. Operating costs for all options are equal.
SOLUTION
We construct a decision tree to advise Hackers’ owner on the best action. Exhibit 3.6 shows the
decision tree for this problem. There are two decision points (shown with the square nodes) and three
chance occurrences (round nodes).
Service
Tutorial:
Decision
Trees
66
exhibit 3.6
section 2
PROCESSES
Decision Tree for Hackers Computer Store Problem
Strong growth
Move
.55
Weak growth
.45
Strong growth
Hackers Computer
Store
Expand
.55
Weak growth
.45
Revenue-Move_Cost
Revenue-Move_Cost
Revenue-Expansion_Cost
Revenue-Expansion_Cost
Expand
Strong growth
Do nothing
.55
Weak growth
.45
Do nothing
Revenue-Expansion_Cost
Revenue
Revenue
The values of each alternative outcome shown on the right of the diagram in Exhibit 3.7 are calculated as follows:
Excel:
Capacity
Excel:
Decision
Trees
ALTERNATIVE
REVENUE
COST
VALUE
Move to new location, strong growth
$195,000 × 5 yrs
$210,000
$765,000
Move to new location, weak growth
$115,000 × 5 yrs
$210,000
$365,000
Expand store, strong growth
$190,000 × 5 yrs
$87,000
$863,000
Expand store, weak growth
$100,000 × 5 yrs
$87,000
$413,000
Do nothing now, strong growth, expand next year
$170,000 × 1 yr +
$190,000 × 4 yrs
$87,000
$843,000
Do nothing now, strong growth, do not expand next year
$170,000 × 5 yrs
$0
$850,000
Do nothing now, weak growth
$105,000 × 5 yrs
$0
$525,000
Working from the rightmost alternatives, which are associated with the decision of whether to
expand, we see that the alternative of doing nothing has a higher value than the expansion alternative.
We therefore eliminate the expansion in the second year alternatives. What this means is that if we do
nothing in the first year and we experience strong growth, then in the second year it makes no sense
to expand.
Now we can calculate the expected values associated with our current decision alternatives. We
simply multiply the value of the alternative by its probability and sum the values. The expected value
for the alternative of moving now is $585,000. The expansion alternative has an expected value of
$660,500, and doing nothing now has an expected value of $703,750. Our analysis indicates that our
best decision is to do nothing (both now and next year)!
Due to the five-year time horizon, it may be useful to consider the time value of the revenue and
cost streams when solving this problem. If we assume a 16 percent interest rate, the first alternative
outcome (move now, strong growth) has a discounted revenue valued at $428,487 (195,000 ×
3.274293654) minus the $210,000 cost to move immediately. Exhibit 3.8 shows the analysis considering
STRATEGIC CAPACITY MANAGEMENT
chapter 3
exhibit 3.7
Decision Tree Analysis
Move
Strong growth
.0.550
$585,000
Weak growth
0.450
Hackers Computer
Store
Strong growth
0.550
Expand
$660,500
Do nothing; $703,750 Weak growth
0.450
Revenue-Move_Cost ⫽ $765,000
Revenue-Move_Cost ⫽ $365,000
Revenue-Expansion_Cost ⫽ $863,000
Revenue-Expansion_Cost ⫽ $413,000
Expand
Strong growth
Do nothing
0.550
$703,750
Weak growth
0.450
Revenue-Expansion_Cost ⫽ $843,000
Do nothing; $850,000
Do nothing
Revenue ⫽ $850,000; P ⫽ 0.550
Revenue ⫽ $525,000; P ⫽ 0.450
exhibit 3.8
Decision Tree Analysis Using Net Present Value Calculations
Move
Strong growth
.0.550
$310,613
Weak growth
0.450
Hackers Computer
Store
Expand
Strong growth
0.550
$402,507
Weak growth
0.450
Revenue-Move_Cost ⫽ $428,487
Revenue-Move_Cost ⫽ $166,544
Revenue-Expansion_Cost ⫽ $535,116
Revenue-Expansion_Cost ⫽ $240,429
Expand
Strong growth
Do nothing
NPV Analysis
Rate ⫽ 16%
67
0.550
$460,857
Weak growth
0.450
Revenue-Expansion_Cost ⫽ $529,874
Do nothing; $556,630
Do nothing
Revenue ⫽ $556,630; P ⫽ 0.550
Revenue ⫽ $343,801; P ⫽ 0.450
the discounted flows. Details of the calculations are given below. Present value table in
Appendix C can be used to look up the discount factors. In order to make our calculations agree
with those completed by Excel, we have used discount factors that are calculated to 10 digits of precision. The only calculation that is a little tricky is the one for revenue when we do nothing now and
expand at the beginning of next year. In this case, we have a revenue stream of $170,000 the first
year, followed by four years at $190,000. The first part of the calculation (170,000 × .862068966)
68
section 2
PROCESSES
discounts the first-year revenue to present. The next part (190,000 × 2.798180638) discounts the next
four years to the start of year two. We then discount this four-year stream to present value.
Excel:
Decision
Trees
ALTERNATIVE
REVENUE
COST
VALUE
Move to new location, strong growth
Move to new location, weak growth
Expand store, strong growth
Expand store, weak growth
Do nothing now, strong growth,
expand next year
$195,000 × 3.274293654
$115,000 × 3.274293654
$190,000 × 3.274293654
$100,000 × 3.274203654
$170,000 × .862068966 +
$190,000 × 2.798180638 ×
.862068966
$170,000 × 3.274293654
$210,000
$210,000
$87,000
$87,000
$87,000 ×
.862068966
$428,487
$166,544
$535,116
$240,429
$529,874
$0
$556,630
$105,000 × 3.274293654
$0
$343,801
Do nothing now, strong growth,
do not expand next year
Do nothing now, weak growth
•
P L A N N I N G S E RV I C E C A PAC I T Y
Capacity Planning in Service
versus Manufacturing
Service
Vol. IX “Service Design
Featuring Hotel Monaco”
Although capacity planning in services is subject to many of the same issues as manufacturing capacity planning, and facility sizing can be done in much the same way, there are
several important differences. Service capacity is more time- and location-dependent, it is
subject to more volatile demand fluctuations, and utilization directly impacts service
quality.
T i m e Unlike goods, services cannot be stored for later use. As such, in services managers
must consider time as one of their supplies. The capacity must be available to produce a
service when it is needed. For example, a customer cannot be given a seat that went
unoccupied on a previous airline flight if the current flight is full. Nor could the customer
purchase a seat on a particular day’s flight and take it home to be used at some later date.
L o c a t i o n In face-to-face settings, the service capacity must be located near the
customer. In manufacturing, production takes place, and then the goods are distributed to
the customer. With services, however, the opposite is true. The capacity to deliver the
service must first be distributed to the customer (either physically or through some
communications medium such as the telephone); then the service can be produced. A hotel
room or rental car that is available in another city is not much use to the customer—it must
be where the customer is when that customer needs it.
V o l a t i l i t y o f D e m a n d The volatility of demand on a service delivery system is
much higher than that on a manufacturing production system for three reasons. First, as just
mentioned, services cannot be stored. This means that inventory cannot smooth the
demand as in manufacturing. The second reason is that the customers interact directly with
the production system—and these customers often have different needs, will have different
levels of experience with the process, and may require different numbers of transactions.
This contributes to greater variability in the processing time required for each customer and
hence greater variability in the minimum capacity needed. The third reason for the greater
STRATEGIC CAPACITY MANAGEMENT
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69
volatility in service demand is that it is directly affected by consumer behavior. Influences
on customer behavior ranging from the weather to a major event can directly affect demand
for different services. Go to any restaurant near your campus during spring break and it will
probably be almost empty. This behavioral effect can be seen over even shorter time frames
such as the lunch-hour rush at a bank’s drive-through window. Because of this volatility,
service capacity is often planned in increments as small as 10 to 30 minutes, as opposed to
the one-week increments more common in manufacturing.
Capacity Utilization and Service Quality
Planning capacity levels for services must consider the day-to-day relationship between
service utilization and service quality. Exhibit 3.9 shows a service situation cast in waiting
line terms (arrival rates and service rates). The best operating point is near 70 percent of the
maximum capacity. This is enough to keep servers busy but allows enough time to serve
customers individually and keep enough capacity in reserve so as not to create too many
managerial headaches. In the critical zone, customers are processed through the system,
but service quality declines. Above the critical zone, the line builds up and it is likely that
many customers may never be served.
The optimal utilization rate is very context specific. Low rates are appropriate when both
the degree of uncertainty and the stakes are high. For example, hospital emergency rooms
and fire departments should aim for low utilization because of the high level of uncertainty
and the life-or-death nature of their activities. Relatively predictable services such as commuter trains or service facilities without customer contact, such as postal sorting operations, can plan to operate much nearer 100 percent utilization. Interestingly, there is a third
group for which high utilization is desirable. All sports teams like sellouts, not only because
of the virtually 100 percent contribution margin of each customer, but because a full house
creates an atmosphere that pleases customers, motivates the home team to perform better,
and boosts future ticket sales. Stage performances and bars share this phenomenon. On the
other hand, many airline passengers feel that a flight is too crowded when the seat next to
theirs is occupied. Airlines capitalize on this response to sell more business-class seats.
Relationship between the Rate of Service Utilization (ρ) and Service Quality
␳ ⫽ 100%
␭
Zone of nonservice
(␮ < ␭)
Critical
zone
␳ ⫽ 70%
Mean arrival
rate (␭)
Zone of service
Mean service rate (␮)
␮
Source: J. Haywood-Farmer and J. Nollet, Services Plus: Effective Service Management
(Boucherville, Quebec, Canada: G. Morin Publisher Ltd., 1991), p. 59.
exhibit 3.9
70
section 2
PROCESSES
S U M M A RY
Strategic capacity planning involves an investment decision that must match resource capabilities to a long-term demand forecast. As discussed in this chapter, factors to be taken
into account in selecting capacity additions for both manufacturing and services include
•
•
•
•
The likely effects of economies of scale.
The effects of learning curves and how to analyze them.
The impact of changing facility focus and balance among production stages.
The degree of flexibility of facilities and the workforce in the operation and its supply system.
For services in particular, a key consideration is the effect of capacity changes on the
quality of the service offering.
Service
K e y Te r m s
Capacity The amount of output that a system is capable of
achieving over a specific period of time.
Strategic capacity planning Determining the overall capacity level of capital-intensive resources that best supports the
company’s long-range competitive strategy.
Best operating level The level of capacity for which the
process was designed and the volume of output at which
average unit cost is minimized.
Capacity utilization rate Measures how close a firm is to its
best operating level.
Capacity focus Can be operationalized through the plantswithin-plants concept, where a plant has several suborganizations specialized for different products—even though they
are under the same roof. This permits finding the best operating level for each suborganization.
Economies of scope Exist when multiple products can be produced at a lower cost in combination than they can separately.
Learning curve A line displaying the relationship between unit
production time and the cumulative number of units produced.
Capacity cushion Capacity in excess of expected demand.
Formula Review
Logarithmic curve:
[3.1]
Yx = K x n
Solved Problems
SOLVED PROBLEM 1
A job applicant is being tested for an assembly line position. Management feels that steady-state
times have been approximately reached after 1,000 performances. Regular assembly line workers are
expected to perform the task within four minutes.
a. If the job applicant performed the first test operation in 10 minutes and the second one in 9 minutes,
should this applicant be hired?
b. What is the expected time that the job applicant would take to finish the 10th unit?
c. What is a significant limitation of this analysis?
STRATEGIC CAPACITY MANAGEMENT
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71
Solution
a. Learning rate = 9 minutes/10 minutes = 90%
From Appendix Exhibit B.1, the time for the 1,000th unit is .3499 × 10 minutes = 3.499 minutes. Yes, hire the person.
b. From Appendix Exhibit B.1, unit 10 at 90% is .7047. Therefore, the time for the 10th unit =
.7047 × 10 = 7.047 minutes.
c. Extrapolating based on just the first two units is unrealistic. More data should be collected to
evaluate the job applicant’s performance.
SOLVED PROBLEM 2
Boeing Aircraft collected the following cost data on the first 8 units of their new business jet.
UNIT NUMBER
COST ($ MILLIONS)
UNIT NUMBER
COST ($ MILLIONS)
1
2
3
4
$100
83
73
62
5
6
7
8
60
57
53
51
a. Estimate the learning curve for the new business jet.
b. Estimate the average cost for the first 1,000 units of the jet.
c. Estimate the cost to produce the 1,000th jet.
Solution
a. First, estimate the learning curve rate by calculating the average learning rate with each doubling of production.
Units 1 to 2 = 83/100 = 83%
Units 2 to 4 = 62/83 = 74.7%
Units 4 to 8 = 51/62 = 82.26%
Average = (83 + 74.4 + 82.6)/3 = 80%
b. The average cost of the first 1,000 units can be estimated using Appendix Exhibit B.2. The cumulative improvement factor for the 1,000th unit at 80 percent learning is 158.7. The cost to
produce the first 1,000 units is
$100M × 158.7 = $15,870M
The average cost for each of the first 1,000 units is
$15,870M/1,000 = $15.9M
c. To estimate the cost to produce the 1,000th unit use Appendix Exhibit B.1.
The unit improvement factor for the 1,000th unit at 80 percent is .1082.
The cost to produce the 1,000th unit is
$100M × .1082 = $10.82M
SOLVED PROBLEM 3
E-Education is a new start-up that develops and markets MBA courses offered over the Internet.
The company is currently located in Chicago and employs 150 people. Due to strong growth the
company needs additional office space. The company has the option of leasing additional space
at its current location in Chicago for the next two years, but after that will need to move to a new
building. Another option the company is considering is moving the entire operation to a small
Midwest town immediately. A third option is for the company to lease a new building in Chicago
immediately. If the company chooses the first option and leases new space at its current location,
it can, at the end of two years, either lease a new building in Chicago or move to the small
Midwest town.
Excel:
Learning
Curves
72
section 2
PROCESSES
The following are some additional facts about the alternatives and current situation:
1 The company has a 75 percent chance of surviving the next two years.
2 Leasing the new space for two years at the current location in Chicago would cost $750,000
per year.
3 Moving the entire operation to a Midwest town would cost $1 million. Leasing space would
run only $500,000 per year.
4 Moving to a new building in Chicago would cost $200,000, and leasing the new building’s
space would cost $650,000 per year.
5 The company can cancel the lease at any time.
6 The company will build its own building in five years, if it survives.
7 Assume all other costs and revenues are the same no matter where the company is located.
What should E-Education do?
Solution
Step 1: Construct a decision tree that considers all of E-Education’s alternatives. The following
shows the tree that has decision points (with the square nodes) followed by chance occurrences
(round nodes). In the case of the first decision point, if the company survives, two additional decision points need consideration.
Lease new space
in Chicago
Survive (.75)
Stay in Chicago
Lease space for two years
Move to Midwest
Survive (.75)
E-Education
$1,500,000
$3,450,000
$2,962,500
Fail (.25)
Survive (.75)
Move to Midwest
town
$4,000,000
$3,112,500
Fail (.25)
Stay in Chicago
Lease new space
$3,650,000
$1,500,000
$3,500,000
$3,125,000
Fail (.25)
$2,000,000
Step 2: Calculate the values of each alternative as follows:
ALTERNATIVE
CALCULATION
VALUE
Stay in Chicago, lease space for two years, survive,
lease new building in Chicago
Stay in Chicago, lease space for two years, survive,
move to Midwest
Stay in Chicago, lease space for two years, fail
Stay in Chicago, lease new building in Chicago, survive
Stay in Chicago, lease new building in Chicago, fail
Move to Midwest, survive
Move to Midwest, fail
(750,000) × 2 + 200,000 +
(650,000) × 3 =
(750,000) × 2 + 1,000,000 +
(500,000) × 3 =
(750,000) × 2 =
200,000 + (650,000) × 5 =
200,000 + (650,000) × 2 =
1,000,000 + (500,000) × 5 =
1,000,000 + (500,000) × 2 =
$3,650,000
$4,000,000
$ 1,500,000
$3,450,000
$ 1,500,000
$3,500,000
$2,000,000
Working from our rightmost alternatives, the first two alternatives end in decision nodes. Because
the first option, staying in Chicago and leasing space for two years, is the lowest cost, this is what
we would do if for the first two years we decide to stay in Chicago. If we fail after the first two
STRATEGIC CAPACITY MANAGEMENT
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chapter 3
years, represented by the third alternative, the cost is only $1,500,000. The expected value of the
first option of staying in Chicago and leasing space for the first two years is .75 × 3,650,000 +
.25 × 1,500,000 = $3,112,500.
The second option, staying in Chicago and leasing a new building now, has an expected value
of .75 × 3,450,000 + .25 × 1,500,000 = $2,962,500.
Finally, the third option of moving to the Midwest immediately has an expected value of .75 ×
3,500,000 + .25 × 2,000,000 = $3,125,000.
From this, it looks like the best alternative is to stay in Chicago and lease a new building
immediately.
Review and Discussion Questions
1 What capacity problems are encountered when a new drug is introduced to the market?
2 List some practical limits to economies of scale; that is, when should a plant stop growing?
3 What are some capacity balance problems faced by the following organizations or facilities?
a. An airline terminal.
b. A university computing lab.
c. A clothing manufacturer.
4 What are some major capacity considerations in a hospital? How do they differ from those
of a factory?
5 Management may choose to build up capacity in anticipation of demand or in response to developing demand. Cite the advantages and disadvantages of both approaches.
6 What is capacity balance? Why is it hard to achieve? What methods are used to deal with
capacity imbalances?
7 What are some reasons for a plant to maintain a capacity cushion? How about a negative
capacity cushion?
8 At first glance, the concepts of the focused factory and capacity flexibility may seem to contradict each other. Do they really?
Problems
1 A time standard was set as 0.20 hour per unit based on the 50th unit produced. If the task has
a 90 percent learning curve, what would be the expected time of the 100th, 200th, and 400th
units?
2 You have just received 10 units of a special subassembly from an electronics manufacturer
at a price of $250 per unit. A new order has also just come in for your company’s product that
uses these subassemblies, and you wish to purchase 40 more to be shipped in lots of 10 units
each. (The subassemblies are bulky, and you need only 10 a month to fill your new order.)
a. Assuming a 70 percent learning curve by your supplier on a similar product last year, how
much should you pay for each lot? Assume that the learning rate of 70 percent applies to
each lot of 10 units, not each unit.
b. Suppose you are the supplier and can produce 20 units now but cannot start production
on the second 20 units for two months. What price would you try to negotiate for the last
20 units?
3 Johnson Industries received a contract to develop and produce four high-intensity longdistance receiver/transmitters for cellular telephones. The first took 2,000 labor hours and
$39,000 worth of purchased and manufactured parts; the second took 1,500 labor hours and
$37,050 in parts; the third took 1,450 labor hours and $31,000 in parts; and the fourth took
1,275 labor hours and $31,492 in parts.
Johnson was asked to bid on a follow-on contract for another dozen receiver/transmitter
units. Ignoring any forgetting factor effects, what should Johnson estimate time and parts
1. 100th = 0.18 hr.
200th = 0.16 hr.
400th = 0.15 hr.
2. a.
1st 10 units = $2,500.00
2nd 10 units = 1,750.00
3rd 10 units = 1,420.50
4th 10 units = 1,225.00
5th 10 units = 1,092.00
b. Between max. of
$4,250 and min. of
$2,645.50.
3. LR parts, 90%; LR labor,
80%; Labor:
11,556 hours. Parts:
$330,876.
74
section 2
4. a. Labor, $570,150.
Materials, 1,356,750
plus something for
profit.
b. Need to consider
forgetting and
relearning. Time and
cost could be much
higher.
5. a. 190/970 = .1958,
PROCESSES
costs to be for the dozen units? (Hint: There are two learning curves—one for labor and one
for parts.)
4 Lambda Computer Products competed for and won a contract to produce two prototype units
of a new type of computer that is based on laser optics rather than on electronic binary bits.
The first unit produced by Lambda took 5,000 hours to produce and required $250,000
worth of material, equipment usage, and supplies. The second unit took 3,500 hours and used
$200,000 worth of materials, equipment usage, and supplies. Labor is $30 per hour.
a. Lambda was asked to present a bid for 10 additional units as soon as the second unit was
completed. Production would start immediately. What would this bid be?
b. Suppose there was a significant delay between the contracts. During this time, personnel
and equipment were reassigned to other projects. Explain how this would affect the subsequent bid.
5 You’ve just completed a pilot run of 10 units of a major product and found the processing
time for each unit was as follows:
from table LR is
UNIT NUMBER
TIME (HOURS)
between 60 and
1
2
3
4
5
6
7
8
9
10
65%.
b. About 8,029 hours.
c. 6.0 hours.
6. a. 70%
b. $145,956,000.
c. Cost .0851 × $12 =
$1,021,200.
970
640
420
380
320
250
220
207
190
190
a. According to the pilot run, what would you estimate the learning rate to be?
b. Based on a, how much time would it take for the next 190 units, assuming no loss of
learning?
c. How much time would it take to make the 1,000th unit?
6 Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could
be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI,
but the bulk of the funding came from a contract with the U.S. Department of Defense
(DoD).
Testing of the laser units has shown that they are effective defense weapons, and through
redesign to add portability and easier field maintenance, the units could be truck-mounted.
DoD has asked LTI to submit a bid for 100 units.
The 20 units that LTI has built so far cost the following amounts and are listed in the order
in which they were produced:
UNIT
NUMBER
1
2
3
4
5
6
7
8
9
10
COST
($ MILLIONS)
$12
10
6
6.5
5.8
6
5
3.6
3.6
4.1
UNIT
NUMBER
COST
($ MILLIONS)
11
12
13
14
15
16
17
18
19
20
$3.9
3.5
3.0
2.8
2.7
2.7
2.3
3.0
2.9
2.6
STRATEGIC CAPACITY MANAGEMENT
7
8
9
10
a. Based on past experience, what is the learning rate?
b. What bid should LTI submit for the total order of 100 units, assuming that learning
continues?
c. What is the cost expected to be for the last unit under the learning rate you estimated?
Jack Simpson, contract negotiator for Nebula Airframe Company, is currently involved in
bidding on a follow-up government contract. In gathering cost data from the first three units,
which Nebula produced under a research and development contract, he found that the first
unit took 2,000 labor hours, the second took 1,800 labor hours, and the third took
1,692 hours.
In a contract for three more units, how many labor hours should Simpson plan for?
Honda Motor Company has discovered a problem in the exhaust system of one of its automobile lines and has voluntarily agreed to make the necessary modifications to conform with
government safety requirements. Standard procedure is for the firm to pay a flat fee to dealers for each modification completed.
Honda is trying to establish a fair amount of compensation to pay dealers and has decided
to choose a number of randomly selected mechanics and observe their performance and
learning rate. Analysis demonstrated that the average learning rate was 90 percent, and
Honda then decided to pay a $60 fee for each repair (3 hours × $20 per flat-rate hour).
Southwest Honda, Inc., has complained to Honda Motor Company about the fee. Six
mechanics, working independently, have completed two modifications each. All took 9 hours
on the average to do the first unit and 6.3 hours to do the second. Southwest refuses to do any
more unless Honda allows at least 4.5 hours. The dealership expects to perform the modification to approximately 300 vehicles.
What is your opinion of Honda’s allowed rate and the mechanics’ performance?
United Research Associates (URA) had received a contract to produce two units of a new
cruise missile guidance control. The first unit took 4,000 hours to complete and cost $30,000
in materials and equipment usage. The second took 3,200 hours and cost $21,000 in materials and equipment usage. Labor cost is charged at $18 per hour.
The prime contractor has now approached URA and asked to submit a bid for the cost of
producing another 20 guidance controls.
a. What will the last unit cost to build?
b. What will be the average time for the 20 missile guidance controls?
c. What will the average cost be for guidance control for the 20 in the contract?
AlwaysRain Irrigation, Inc., would like to determine capacity requirements for the next four
years. Currently two production lines are in place for bronze and plastic sprinklers. Three
types of sprinklers are available in both bronze and plastic: 90-degree nozzle sprinklers,
180-degree nozzle sprinklers, and 360-degree nozzle sprinklers. Management has forecast
demand for the next four years as follows:
YEARLY DEMAND
Plastic 90
Plastic 180
Plastic 360
Bronze 90
Bronze 180
Bronze 360
1 (IN 000S)
2 (IN 000S)
3 (IN 000S)
4 (IN 000S)
32
15
50
7
3
11
44
16
55
8
4
12
55
17
64
9
5
15
56
18
67
10
6
18
75
chapter 3
Both production lines can produce all the different types of nozzles. Each bronze machine
requires two operators and can produce up to 12,000 sprinklers. The plastic injection molding machine requires four operators and can produce up to 200,000 sprinklers. Three bronze
machines and only one injection molding machine are available. What are the capacity
requirements for the next four years? (Assume that there is no learning.)
7. 4,710 hours.
8. Learning rate = 70%;
unreasonable to ask
for 4.5 hours. After 25,
average repetitions
time is about 3 hours.
9. a. Cost of 22nd unit =
$32,732.40.
b. 1,886 hours.
c. Average cost =
$43,126.50.
10. See ISM.
76
section 2
11. Not enough capacity
after second year.
PROCESSES
11 Suppose that AlwaysRain Irrigation’s marketing department will undertake an intense ad
campaign for the bronze sprinklers, which are more expensive but also more durable than the
plastic ones. Forecast demand for the next four years is
YEARLY DEMAND
Plastic 90
Plastic 180
Plastic 360
Bronze 90
Bronze 180
Bronze 360
12. No, there is additional
need after the third
year.
13. There is a need for
additional employees
in the fourth year.
14. Expected NPV—small
$4.8 million. Expected
NPV—large $2.6
million.
15. See ISM. Rezoned
shopping center =
$4.3 million. Rezoned
apartments =
1 (IN 000S)
2 (IN 000S)
3 (IN 000S)
4 (IN 000S)
32
15
50
11
6
15
44
16
55
15
5
16
55
17
64
18
6
17
56
18
67
23
9
20
What are the capacity implications of the marketing campaign (assume no learning)?
12 In anticipation of the ad campaign, AlwaysRain bought an additional bronze machine. Will
this be enough to ensure that enough capacity is available?
13 Suppose that operators have enough training to operate both the bronze machines and the
injection molding machine for the plastic sprinklers. Currently AlwaysRain has 10 such
employees. In anticipation of the ad campaign described in Problem 11, management
approved the purchase of two additional bronze machines. What are the labor requirement
implications?
14 Expando, Inc., is considering the possibility of building an additional factory that would produce a new addition to their product line. The company is currently considering two options.
The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value
of future revenues) with the small facility. On the other hand, if demand is high, it expects $12
million in discounted revenues using the small facility. The second option is to build a large
factory at a cost of $9 million. Were demand to be low, the company would expect $10 million in discounted revenues with the large plant. If demand is high, the company estimates that
the discounted revenues would be $14 million. In either case, the probability of demand being
high is .40, and the probability of it being low is .60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce
these new products. Construct a decision tree to help Expando make the best decision.
15 A builder has located a piece of property that she would like to buy and eventually build on.
The land is currently zoned for four homes per acre, but she is planning to request new zoning. What she builds depends on approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the decision process has been reduced to the
following costs, alternatives, and probabilities:
$3.9 million. No
Cost of land: $2 million.
rezoning = $.4 million.
Probability of rezoning: .60.
Expected results:
.60(1.3) + 0.40(.4) =
$.94 million.
If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of
$1 million.
If the land is rezoned, the contractor must decide whether to build a shopping center or
1,500 apartments that the tentative plan shows would be possible. If she builds a shopping
center, there is a 70 percent chance that she can sell the shopping center to a large department
chain for $4 million over her construction cost, which excludes the land; and there is a
30 percent chance that she can sell it to an insurance company for $5 million over her construction cost (also excluding the land). If, instead of the shopping center, she decides to
build the 1,500 apartments, she places probabilities on the profits as follows: There is a
60 percent chance that she can sell the apartments to a real estate investment corporation for
$3,000 each over her construction cost; there is a 40 percent chance that she can get only
$2,000 each over her construction cost. (Both exclude the land cost.)
STRATEGIC CAPACITY MANAGEMENT
77
chapter 3
If the land is not rezoned, she will comply with the existing zoning restrictions and simply build 600 homes, on which she expects to make $4,000 over the construction cost on
each one (excluding the cost of land).
Draw a decision tree of the problem and determine the best solution and the expected net
profit.
CASE:
Shouldice Hospital—A Cut Above
“Shouldice Hospital, the house that hernias built, is a converted country estate which gives the hospital ‘a country
club’ appeal.”
A quote from American Medical News
Shouldice Hospital in Canada is widely known for one
thing—hernia repair! In fact, that is the only operation it performs, and it performs a great many of them. Over the past
two decades this small 90-bed hospital has averaged 7,000
operations annually. Last year, it had a record year and performed nearly 7,500 operations. Patients’ ties to Shouldice do
not end when they leave the hospital. Every year the gala
Hernia Reunion dinner (with complimentary hernia
inspection) draws in excess of 1,000 former patients, some of
whom have been attending the event for over 30 years.
A number of notable features in Shouldice’s service delivery system contribute to its success. (1) Shouldice accepts
only patients with the uncomplicated external hernias, and it
uses a superior technique developed for this type of hernia by
Dr. Shouldice during World War II. (2) Patients are subject to
early ambulation, which promotes healing. (Patients literally
walk off the operating table and engage in light exercise
throughout their stay, which lasts only three days.) (3) Its
country club atmosphere, gregarious nursing staff, and builtin socializing make a surprisingly pleasant experience out of
an inherently unpleasant medical problem. Regular times are
set aside for tea, cookies, and socializing. All patients are
paired up with a roommate with similar background and
interests.
The Production System
The medical facilities at Shouldice consist of five operating
rooms, a patient recovery room, a laboratory, and six examination rooms. Shouldice performs, on average, 150 operations per week, with patients generally staying at the hospital
for three days. Although operations are performed only five
days a week, the remainder of the hospital is in operation continuously to attend to recovering patients.
An operation at Shouldice Hospital is performed by one
of the 12 full-time surgeons assisted by one of seven parttime assistant surgeons. Surgeons generally take about one
hour to prepare for and perform each hernia operation, and
they operate on four patients per day. The surgeons’ day ends
at 4 P.M., although they can expect to be on call every 14th
night and every 10th weekend.
Excel:
Shouldice
Hosp
Vol. III.
“Shouldice Hospital”
The Shouldice Experience
Each patient undergoes a screening exam prior to setting a
date for his or her operation. Patients in the Toronto area are
encouraged to walk in for the diagnosis. Examinations are
done between 9 A.M. and 3:30 P.M. Monday through Friday,
and between 10 A.M. and 2 P.M. on Saturday. Out-of-town patients are mailed a medical information questionnaire (also
available over the Internet), which is used for the diagnosis. A
small percentage of the patients who are overweight or otherwise represent an undue medical risk are refused treatment.
The remaining patients receive confirmation cards with the
scheduled dates for their operations. A patient’s folder is
transferred to the reception desk once an arrival date is
confirmed.
Patients arrive at the clinic between 1 and 3 P.M. the day
before their surgery. After a short wait, they receive a brief
preoperative examination. They are then sent to an admissions clerk to complete any necessary paperwork. Patients
are next directed to one of the two nurses’ stations for blood
and urine tests and then are shown to their rooms. They spend
the remaining time before orientation getting settled and acquainting themselves with their roommates.
Orientation begins at 5 P.M., followed by dinner in the
common dining room. Later in the evening, at 9 P.M., patients
gather in the lounge area for tea and cookies. Here new patients can talk with patients who have already had their
surgery. Bedtime is between 9:30 and 10 P.M.
On the day of the operation, patients with early operations are awakened at 5:30 A.M. for preoperative sedation.
The first operations begin at 7:30 A.M. Shortly before an operation starts, the patient is administered a local anesthetic,
leaving him or her alert and fully aware of the proceedings.
At the conclusion of the operation, the patient is invited to
walk from the operating table to a nearby wheelchair, which
is waiting to return the patient to his or her room. After a
brief period of rest, the patient is encouraged to get up and
start exercising. By 9 P.M. that day, he or she is in the lounge
78
section 2
PROCESSES
The administrator of the hospital, however, is concerned
about maintaining control over the quality of the service
delivered. He thinks the facility is already getting very good
utilization. The doctors and the staff are happy with their
jobs, and the patients are satisfied with the service. According to him, further expansion of capacity might make it hard
to maintain the same kind of working relationships and
attitudes.
having cookies and tea and talking with new, incoming
patients.
The skin clips holding the incision together are loosened,
and some are removed, the next day. The remainder are removed the following morning just before the patient is
discharged.
When Shouldice Hospital started, the average hospital
stay for hernia surgery was three weeks. Today, many institutions push “same day surgery” for a variety of reasons.
Shouldice Hospital firmly believes that this is not in the best
interests of patients, and is committed to its three-day
process. Shouldice’s postoperative rehabilitation program is
designed to enable the patient to resume normal activities
with minimal interruption and discomfort. Shouldice patients
frequently return to work in a few days; the average total time
off is eight days.
Questions
Exhibit 3.10 is a room-occupancy table for the existing system. Each row in the table follows the patients that checked in
on a given day. The columns indicate the number of patients
in the hospital on a given day. For example, the first row of the
table shows that 30 people checked in on Monday and were in
the hospital for Monday, Tuesday, and Wednesday. By summing the columns of the table for Wednesday, we see that
there are 90 patients staying in the hospital that day.
1 How well is the hospital currently utilizing its beds?
2 Develop a similar table to show the effects of adding
operations on Saturday. (Assume that 30 operations
would still be performed each day.) How would this
affect the utilization of the bed capacity? Is this capacity sufficient for the additional patients?
3 Now look at the effect of increasing the number of
beds by 50 percent. How many operations could the
hospital perform per day before running out of bed capacity? (Assume operations are performed five days
per week, with the same number performed on each
day.) How well would the new resources be utilized
“It is interesting to note that approximately 1 out of every
100 Shouldice patients is a medical doctor.”
Future Plans
The management of Shouldice is thinking of expanding the
hospital’s capacity to serve considerable unsatisfied demand.
To this effect, the vice president is seriously considering two
options. The first involves adding one more day of operations
(Saturday) to the existing five-day schedule, which would increase capacity by 20 percent. The second option is to add
another floor of rooms to the hospital, increasing the number
of beds by 50 percent. This would require more aggressive
scheduling of the operating rooms.
exhibit 3.10
Operations with 90 Beds (30 patients per day)
BEDS REQUIRED
CHECK-IN DAY
Monday
MONDAY
TUESDAY
WEDNESDAY
30
30
30
30
30
30
30
30
30
30
30
Tuesday
Wednesday
Thursday
THURSDAY
FRIDAY
SATURDAY
SUNDAY
30
Friday
Saturday
Sunday
30
30
Total
60
90
30
90
90
60
30
30
STRATEGIC CAPACITY MANAGEMENT
relative to the current operation? Could the hospital
really perform this many operations? Why? (Hint:
Look at the capacity of the 12 surgeons and the five
operating rooms.)
4 Although financial data are sketchy, an estimate from
a construction company indicates that adding bed
capacity would cost about $100,000 per bed. In
chapter 3
79
addition, the rate charged for the hernia surgery
varies between about $900 and $2,000 (U.S. dollars),
with an average rate of $1,300 per operation. The
surgeons are paid a flat $600 per operation. Due to all
the uncertainties in government health care legislation, Shouldice would like to justify any expansion
within a five-year time period.
Selected Bibliography
Wright, T. P. “Factors Affecting the Cost of Airplanes.” Journal of Aeronautical Sciences, February 1936, pp. 122–128.
Yu-Lee, R. T. Essentials of Capacity Management. NewYork: Wiley, 2002.